filter mysql database query results in the browser in real time

What web development tools do I need in order to create a web page where the user can filter the database query results client-side in real time, without resubmitting the search? I am thinking of something like sidestep.com where after the initial search is done the can narrow results by clicking checkboxes and filling in fields while they watch their results narrow in the browser winodow without ever having to refresh or resubmit.

This project ist starting its life on a LAN with a very small database so performance is not much of an issue. My challenge is that I only occasionally create web pages and am hoping for a guide that will direct me to the right libraries and such that I might need to learn about. ?ajax, jquery, javascript, spry?

Googling is getting me no where because I am using 3g on a 12 hr train ride and don't know the right search terms. Any search direction or URLs would be appreciated.

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